[Insight-users] Finding saddle points in a 2D image

[Liam Kurmos]

Hi Luis,

I intend to follow this approach for finding the critical points.

On Sun, Apr 25, 2010 at 11:10 PM, Luis Ibanez <luis.ibanez at kitware.com> wrote:
>
>
> Hi Roman,
>
> You can find Saddle-like points by using
> the Hessian image filter:
>
> http://www.itk.org/Doxygen/html/classitk_1_1HessianRecursiveGaussianImageFilter.html
>
> and then computing Eigen analysis for the
> Hessian matrices at every pixels.
>
> Whenever you find that your two eigen values
> have opposite signs, then you are in a Saddle-like
> point.

am i right in thinking that in the 3D case there will be 3 eigen
values, and that a saddle occurs when any 1 is opposite to the other
two?

Liam

>
>
> You can compute the Eigen analysis at every
> pixel by using the class
> http://www.itk.org/Doxygen/html/classitk_1_1SymmetricEigenAnalysis.html
>
> or you can generate a full image by using the class
> http://www.itk.org/Doxygen/html/classitk_1_1SymmetricEigenAnalysisImageFilter.html
>
> The first option will require less memory.
>
>
>      Regards,
>
>
>            Luis
>
>
> ---------------------------------------------------------------------------------------
> On Thu, Apr 22, 2010 at 10:09 AM, Roman Grothausmann
> <roman.grothausmann at helmholtz-berlin.de> wrote:
>>
>> Dear Richard,
>>
>>
>> Many thanks for Your answers. Recommending the watershed filter for this
>> was a great hint. I hadn't realized (since I was not looking for a
>> segmentation) that the borderline of the watershed of the inverted image
>> is exactly what I'm looking for.
>>
>> Still I'm wondering how I could find the saddle points (not the regional
>> minima) of a 2D image (eg. point 0,0 of the plot of the function
>> x*x-y*y). If I'm not mistaken those are the points where a watershed
>> border starts when two basins meet. So kind of the origins of the
>> watershed borderlines.
>>
>> Many thanks again.
>> Roman
>>
>> Richard Beare wrote:
>>>
>>> Hi,
>>> I'm not entirely sure what problem you are trying to solve, but there
>>> may be a simple approach if you outline it in more detail. The
>>> discussion of gradient descent makes me wonder whether you might be
>>> interested in watershed approaches, which are sometimes discussed in
>>> terms of gradient descent but are  more usefully implemented as
>>> gradient ascent.. They are likely to be useful if you have a
>>> segmentation problem.
>>>
>>> Anyhow - regional minima can be found using a number of filters -
>>> search for RegionalMinima in documentation.
>>>
>>> On 4/22/10, Roman Grothausmann <roman.grothausmann at helmholtz-berlin.de>
>>> wrote:
>>>>
>>>> Dear mailing list members,
>>>>
>>>>
>>>> How can I find saddle points and image border pixels with minimum
>>>> gradient in a 2D image? I need those as starting points for tracing the
>>>> gradient decent (as is done in the Random access iteration example in
>>>> the user guide) because I want to detect valley traces in a 2D image
>>>> that originate from saddle points (for no border pixels) or pixels with
>>>> minimum gradient (for image border pixels).
>>>> Is there a way to find these two types of special points with ITK?
>>>>
>>>> Any help is very much appreciated
>>>> Roman
>>>>
>>>> --
>>>> Roman Grothausmann
>>>>
>>>> Helmholtz-Zentrum Berlin für Materialien und Energie GmbH
>>>> Bereich Funktionale Materialien
>>>> Institut für angewandte Materialforschung
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>>>>
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>>>> Fax.: +49-(0)30-8062-3059
>>>>
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>>>
>>>
>>
>> --
>> Roman Grothausmann
>>
>> Helmholtz-Zentrum Berlin für Materialien und Energie GmbH
>> Bereich Funktionale Materialien
>> Institut für angewandte Materialforschung
>> Hahn-Meitner-Platz 1
>> D-14109 Berlin
>>
>> Tel.: +49-(0)30-8062-2816
>> Fax.: +49-(0)30-8062-3059
>>
>> Vorsitzender des Aufsichtsrats: Prof. Dr. Dr. h.c. mult. Joachim Treusch
>> Stellvertretende Vorsitzende: Dr. Beatrix Vierkorn-Rudolph
>> Geschäftsführer: Prof. Dr. Anke Rita Kaysser-Pyzalla, Prof. Dr. Dr. h.c.
>> Wolfgang Eberhardt, Dr. Ulrich Breuer
>> Sitz der Gesellschaft: Berlin
>> Handelsregister: AG Charlottenburg, 89 HRB 5583
>>
>>
>> _____________________________________
>> Powered by www.kitware.com
>>
>> Visit other Kitware open-source projects at
>> http://www.kitware.com/opensource/opensource.html
>>
>> Kitware offers ITK Training Courses, for more information visit:
>> http://www.kitware.com/products/protraining.html
>>
>> Please keep messages on-topic and check the ITK FAQ at:
>> http://www.itk.org/Wiki/ITK_FAQ
>>
>> Follow this link to subscribe/unsubscribe:
>> http://www.itk.org/mailman/listinfo/insight-users
>
>
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